How To Understand The Doppler Effect

Transcription

1 11.2 THE DOPPLER EFFECT Notes III. HOW THE DOPPLER EFFECT WORKS WITH SOUND A. SOUND FREQUENCY AND PITCH The frequency of sound waves is proportional to the pitch that we hear. DEMO Tuning Forks f = higher pitch and f = lower pitch You know that the pitch of the note from the siren of a fast-travelling ambulance or police car appears to a stationary observer to drop suddenly as it passes. This means that the frequency changes as the object passes. But the frequency does not really change (ask the person driving the vehicle!) DEFINE: Doppler Effect : The apparent change in the frequency of a wave motion when there is relative motion between the source and the observer Occurs with electromagnetic waves as well as with sound and water waves. The human ear is amazingly sensitive to small changes in pitch. The human ear can hear frequencies between about 20 Hz and 20 khz (< 20 Hz is called infrasonic, and > 20 khz is called ultrasonic). The equations here hold for sound waves. Figures (a) and (b) show a truck sounding a siren at rest and moving. In figure (b), the wavelengths in front of the truck are shorter than the ones behind it. The speed of sound is the same ahead of and behind the truck, and v = fλ. Therefore, f and λ are inversely proportional. So, λ means f which means pitch (behind) and λ means f which means pitch (in front). Source: Physics for the IB Diploma Study Guide, Kirk Source: Physics, 8 th Ed, Cutnell & Johnson 1

2 Source: Physics for the IB Diploma, 5 th Ed, Tsokos B. STATIONARY OBSERVER AND A MOVING SOURCE Generally, remember: u s so and In this case: Let v = speed of wave Let u s = speed of source v In 1 s, first wave moves v towards observer In 1 s, source emits f waves In 1 s, source moves u s towards observer u s v - u s f wavefronts in this distance f waves contained in a distance v - u s separation of waves (wavelength) is so source moving towards observer source moving away from observer Check that if u s = 0, then f = f? YES. NOTE THAT: λ λ Graph of f against d looks like this: Source: Physics for the IB Diploma, 5 th Ed, Tsokos 2

3 Source: Physics, 8 th Ed, Cutnell & Johnson C. MOVING OBSERVER AND A STATIONARY SOURCE Let u 0 = speed of observer approaching source = u s Think of as a moving source (relative speeds are what is important; distance closing between observer and source) Observer measures higher waves speed = v + u 0 So, becomes or observer moving towards source observer moving away from source NOTE THAT: λ = λ WATCH AP LESSON 45 SOUND WAVES AND THE DOPPLER EFFECT DO HW #5,8 IV. HOW THE DOPPLER EFFECT WORKS WITH EM WAVES A. LIGHT FREQUENCY AND COLOR REMEMBER: The speed of EM waves is x 10 8 m/s = c. f = reds and oranges f = blues and purples LIGHT, SINCE A WAVE, UNDERGOES A DOPPLER SHIFT ALSO! 3

4 B. THE RED SHIFT OF THE UNIVERSE In the Doppler shift for sound the velocities, u o and u s are always measured relative to the air. There is also a Doppler Effect for electromagnetic waves in empty space, such as light waves or radio waves. In this case there is no medium that we can use to measure velocities and all that matters is the relative velocity of the source and receiver. Note this was not the case with sound, because we always incorporated the speed of sound which was determined mainly by the medium and its temperature. Provided the speed of the source or observer << c, the Doppler effect for EM waves is given by the following: where v = speed of source or observer c = speed of light f = frequency emitted Remember the EM visible light spectrum (from about 4 x Hz to about 7.9 x Hz). Source: Physics, 8 th Ed, Cutnell & Johnson Astronomers use the Doppler effect for light to calculate speeds of distant stars and galaxies. Astronomers know the chemical makeup of stars and hence their true color. By comparing the line spectrum of light from the star with light from a laboratory source, the Doppler shift of the star's light can be measured. Then the speed of the star can be calculated! Stars moving towards Earth show a blue shift. This is because the wavelengths of light emitted by the star are shorter than if the star had been at rest (frequency is higher, wavelength is shorter). So the spectrum is shifted towards shorter wavelengths, i.e. to the blue end of the spectrum. Stars moving away from the Earth show a red shift. The emitted waves have a longer wavelength than if the star had been at rest, so the spectrum is shifted towards longer wavelengths, i.e. towards the red end of the spectrum. Astronomers have discovered that all the distant galaxies are moving away from us and by measuring their red shifts, they have estimated their speeds. The furthermost galaxies have been estimated to have speeds approaching the speed of light. 4

5 V. OTHER USES AND APPLICATIONS OF THE DOPPLER EFFECT Besides using the Doppler Effect to determine recession speeds of distant celestial bodies, it is also used in: - Determining the speed of rotation of the sun. Photographs are taken of opposite edges of the sun; each contains absorption lines due to elements such as iron vaporized in the sun, and also some absorption lines due to oxygen in the earth s atmosphere. When the two photographs are put together so that the oxygen lines coincide, the iron lines in the two photographs are displaced relative to one another. Measurements show a rotational speed of about 2 kms Radar speed guns. Microwaves are emitted from a transmitter in short bursts. Each burst reflects off any obstacle in the path of the microwaves. In between sending out bursts, the transmitter is open to detect reflected microwaves. If the reflection is caused by a moving obstacle, the reflected microwaves are Doppler-shifted. By measuring the Doppler shift the speed at which the obstacle moves (along the line between it and the transmitter/receiver) can be calculated. - Medicine. Measuring the speed of blood flow through arteries. - Meteorology. Wind fields in thunderstorms are observed to determine whether there is rotation in the cloud indicating the presence of a tornado. Source: DO HW #10 5